A Generalization of the Erd\"{o}s-Ko-Rado Theorem

TL;DR

This paper generalizes the Erdős-Ko-Rado theorem by characterizing maximum independent sets and providing an upper bound for the chromatic number of local Kneser graphs.

Contribution

It introduces a generalization of the Erdős-Ko-Rado theorem and characterizes maximum independent sets in local Kneser graphs, along with an upper bound for their chromatic number.

Findings

Characterization of maximum independent sets in local Kneser graphs

An upper bound for the chromatic number of these graphs

Extension of Erdős-Ko-Rado theorem to a broader class of graphs

Abstract

In this note, we investigate some properties of local Kneser graphs defined in [8]. In this regard, as a generalization of the Erd${\rm \ddot{o}}$s-Ko-Rado theorem, we characterize the maximum independent sets of local Kneser graphs. Next, we present an upper bound for their chromatic number.